كتاب Design, Modeling and Control of Nanopositioning Systems
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 كتاب Design, Modeling and Control of Nanopositioning Systems

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مُساهمةموضوع: كتاب Design, Modeling and Control of Nanopositioning Systems    كتاب Design, Modeling and Control of Nanopositioning Systems  Emptyالسبت 14 نوفمبر 2020, 12:23 pm

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Design, Modeling and Control of Nanopositioning Systems
Advances in Industrial Control
Andrew J. Fleming
Kam K. Leang  

كتاب Design, Modeling and Control of Nanopositioning Systems  D_m_a_11
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Contents
1 Introduction 1
1.1 Introduction to Nanotechnology . 1
1.2 Introduction to Nanopositioning . 2
1.3 Scanning Probe Microscopy 3
1.4 Challenges with Nanopositioning Systems 7
1.4.1 Hysteresis . 7
1.4.2 Creep . 7
1.4.3 Thermal Drift . 8
1.4.4 Mechanical Resonance . 9
1.5 Control of Nanopositioning Systems 10
1.5.1 Feedback Control 10
1.5.2 Feedforward Control 12
1.6 Book Summary . 13
1.6.1 Assumed Knowledge 13
1.6.2 Content Summary 13
References . 14
2 Piezoelectric Transducers 17
2.1 The Piezoelectric Effect . 17
2.2 Piezoelectric Compositions 20
2.3 Manufacturing Piezoelectric Ceramics . 22
2.4 Piezoelectric Transducers 23
2.5 Application Considerations 26
2.5.1 Mounting 27
2.5.2 Stroke Versus Force 27
2.5.3 Preload and Flexures 29
2.5.4 Electrical Considerations . 30
2.5.5 Self-Heating Considerations . 30
2.6 Response of Piezoelectric Actuators 31
2.6.1 Hysteresis . 31
2.6.2 Creep . 32
2.6.3 Temperature Dependence . 33
2.6.4 Vibrational Dynamics . 34
2.6.5 Electrical Bandwidth 35
ix2.7 Modeling Creep and Vibration in Piezoelectric Actuators . 35
2.8 Chapter Summary . 39
References . 39
3 Types of Nanopositioners 43
3.1 Piezoelectric Tube Nanopositioners . 43
3.1.1 63 mm Piezoelectric Tube 45
3.1.2 40 mm Piezoelectric Tube Nanopositioner . 46
3.2 Piezoelectric Stack Nanopositioners 47
3.2.1 Phyisk Instrumente P-734 Nanopositioner . 49
3.2.2 Phyisk Instrumente P-733.3DD Nanopositioner 49
3.2.3 Vertical Nanopositioners . 50
3.2.4 Rotational Nanopositioners 51
3.2.5 Low Temperature and UHV Nanopositioners . 53
3.2.6 Tilting Nanopositioners 53
3.2.7 Optical Objective Nanopositioners 53
References . 55
4 Mechanical Design: Flexure-Based Nanopositioners . 57
4.1 Introduction . 57
4.2 Operating Environment . 58
4.3 Methods for Actuation 61
4.4 Flexure Hinges . 62
4.4.1 Introduction 62
4.4.2 Types of Flexures 64
4.4.3 Flexure Hinge Compliance Equations 65
4.4.4 Stiff Out-of-Plane Flexure Designs 73
4.4.5 Failure Considerations . 74
4.4.6 Finite Element Approach for Flexure Design . 75
4.5 Material Considerations . 75
4.5.1 Materials for Flexure and Platform Design . 75
4.5.2 Thermal Stability of Materials . 77
4.6 Manufacturing Techniques . 78
4.7 Design Example: A High-Speed Serial-Kinematic
Nanopositioner . 79
4.7.1 State-of-the-Art Designs 79
4.7.2 Tradeoffs and Limitations in Speed 81
4.7.3 Serial- Versus Parallel-Kinematic
Configurations 83
4.7.4 Piezoactuator Considerations 84
4.7.5 Preloading Piezo-Stack Actuators . 85
4.7.6 Flexure Design for Lateral Positioning 86
4.7.7 Design of Vertical Stage . 94
4.7.8 Fabrication and Assembly 97
x Contents4.7.9 Drive Electronics 98
4.7.10 Experimental Results 99
4.8 Chapter Summary . 100
References . 101
5 Position Sensors . 103
5.1 Introduction . 103
5.2 Sensor Characteristics 105
5.2.1 Calibration and Nonlinearity . 105
5.2.2 Drift and Stability 107
5.2.3 Bandwidth . 109
5.2.4 Noise . 110
5.2.5 Resolution . 113
5.2.6 Combining Errors 116
5.2.7 Metrological Traceability . 117
5.3 Nanometer Position Sensors 118
5.3.1 Resistive Strain Sensors 118
5.3.2 Piezoresistive Strain Sensors 121
5.3.3 Piezoelectric Strain Sensors . 123
5.3.4 Capacitive Sensors . 127
5.3.5 MEMs Capacitive and Thermal Sensors . 133
5.3.6 Eddy-Current Sensors . 134
5.3.7 Linear Variable Displacement Transformers 137
5.3.8 Laser Interferometers 140
5.3.9 Linear Encoders . 144
5.4 Comparison and Summary . 147
5.5 Outlook and Future Requirements 148
References . 150
6 Shunt Control 155
6.1 Introduction . 155
6.2 Shunt Circuit Modeling . 157
6.2.1 Open-Loop . 157
6.2.2 Shunt Damping 159
6.3 Implementation . 164
6.4 Experimental Results . 165
6.4.1 Tube Dynamics 166
6.4.2 Amplifier Performance 167
6.4.3 Shunt Damping Performance 168
6.5 Chapter Summary . 173
References . 173
Contents xi7 Feedback Control 175
7.1 Introduction . 175
7.2 Experimental Setup 178
7.3 PI Control 180
7.4 PI Control with Notch Filters . 181
7.5 PI Control with IRC Damping 183
7.6 Performance Comparison 187
7.7 Noise and Resolution 188
7.8 Analog Implementation . 193
7.9 Application to AFM Imaging . 195
7.10 Repetitive Control . 196
7.10.1 Introduction 196
7.10.2 Repetitive Control Concept and Stability
Considerations 198
7.10.3 Dual-Stage Repetitive Control . 201
7.10.4 Handling Hysteresis . 205
7.10.5 Design and Implementation . 205
7.10.6 Experimental Results and Discussion . 214
7.11 Summary . 216
References . 216
8 Force Feedback Control . 221
8.1 Introduction . 221
8.2 Modeling . 223
8.2.1 Actuator Dynamics . 223
8.2.2 Sensor Dynamics 225
8.2.3 Sensor Noise . 226
8.2.4 Mechanical Dynamics . 227
8.2.5 System Properties 228
8.2.6 Example System . 230
8.3 Damping Control . 230
8.4 Tracking Control . 232
8.4.1 Relationship Between Force and Displacement 233
8.4.2 Integral Displacement Feedback 235
8.4.3 Direct Tracking Control 235
8.4.4 Dual Sensor Feedback . 237
8.4.5 Low Frequency Bypass 239
8.4.6 Feedforward Inputs . 240
8.4.7 Higher-Order Modes 241
8.5 Experimental Results . 241
8.5.1 Experimental Nanopositioner 241
8.5.2 Actuators and Force Sensors . 242
xii Contents8.5.3 Control Design 244
8.5.4 Noise Performance . 245
8.6 Chapter Summary . 247
References . 248
9 Feedforward Control . 251
9.1 Why Feedforward? 251
9.2 Modeling for Feedforward Control . 252
9.3 Feedforward Control of Dynamics and Hysteresis . 252
9.3.1 Simple DC-Gain Feedforward Control 252
9.3.2 An Inversion-Based Feedforward Approach
for Linear Dynamics 253
9.3.3 Frequency-Weighted Inversion: The Optimal
Inverse 256
9.3.4 Application to AFM Imaging 256
9.4 Feedforward and Feedback Control . 258
9.4.1 Application to AFM Imaging 261
9.5 Iterative Feedforward Control . 261
9.5.1 The ILC Problem 263
9.5.2 Model-Based ILC 265
9.5.3 Nonlinear ILC 267
9.5.4 Conclusions 271
References . 271
10 Command Shaping . 275
10.1 Introduction . 275
10.1.1 Background 275
10.1.2 The Optimal Periodic Input . 279
10.2 Signal Optimization . 280
10.3 Frequency Domain Cost Functions . 282
10.3.1 Background: Discrete Fourier Series . 282
10.3.2 Minimizing Signal Power . 283
10.3.3 Minimizing Frequency Weighted Power 284
10.3.4 Minimizing Velocity and Acceleration 285
10.3.5 Single-Sided Frequency Domain Calculations . 286
10.4 Time Domain Cost Function . 286
10.4.1 Minimum Velocity . 287
10.4.2 Minimum Acceleration 288
10.4.3 Frequency Weighted Objectives 288
10.5 Application to Scan Generation . 288
10.5.1 Choosing b and K 290
10.5.2 Improving Feedback and Feedforward
Controllers . 292
10.6 Comparison to Other Techniques 293
Contents xiii10.7 Experimental Application 295
10.8 Chapter Summary . 297
References . 297
11 Hysteresis Modeling and Control 299
11.1 Introduction . 299
11.2 Modeling Hysteresis . 300
11.2.1 Simple Polynomial Model 300
11.2.2 Maxwell Slip Model 300
11.2.3 Duhem Model . 301
11.2.4 Preisach Model 302
11.2.5 Classical Prandlt-Ishlinksii Model . 306
11.3 Feedforward Hysteresis Compensation 307
11.3.1 Feedforward Control Using the Presiach Model . 307
11.3.2 Feedforward Control Using
the Prandlt-Ishlinksii Model . 309
11.4 Chapter Summary . 315
References . 315
12 Charge Drives 317
12.1 Introduction . 317
12.2 Charge Drives . 318
12.3 Application to Piezoelectric Stack Nanopositioners 322
12.4 Application to Piezoelectric Tube Nanopositioners 325
12.5 Alternative Electrode Configurations 328
12.5.1 Grounded Internal Electrode . 328
12.5.2 Quartered Internal Electrode . 330
12.6 Charge Versus Voltage . 332
12.6.1 Advantages . 332
12.6.2 Disadvantages . 333
12.7 Impact on Closed-Loop Control . 334
12.8 Chapter Summary . 335
References . 335
13 Noise in Nanopositioning Systems 337
13.1 Introduction . 337
13.2 Review of Random Processes . 338
13.2.1 Probability Distributions . 339
13.2.2 Expected Value, Moments, Variance, and RMS . 339
13.2.3 Gaussian Random Variables . 341
13.2.4 Continuous Random Processes . 343
13.2.5 Joint Density Functions and Stationarity 343
13.2.6 Correlation Functions . 344
13.2.7 Gaussian Random Processes . 344
xiv Contents13.2.8 Power Spectral Density 345
13.2.9 Filtered Random Processes 347
13.2.10 White Noise 348
13.2.11 Spectral Density in V/
ffiffiffiffiffiffi
pHz . 349
13.2.12 Single- and Double-Sided Spectra . 349
13.3 Resolution and Noise 351
13.4 Sources of Nanopositioning Noise . 352
13.4.1 Sensor Noise . 353
13.4.2 External Noise 354
13.4.3 Amplifier Noise . 354
13.5 Closed-Loop Position Noise 359
13.5.1 Noise Sensitivity Functions . 359
13.5.2 Closed-Loop Position Noise Spectral Density . 360
13.5.3 Closed-Loop Noise Approximations
with Integral Control 361
13.5.4 Closed-Loop Position Noise Variance 362
13.5.5 A Note on Units . 364
13.6 Simulation Examples . 364
13.6.1 Integral Controller Noise Simulation . 364
13.6.2 Noise Simulation with Inverse Model Controller . 366
13.6.3 Feedback Versus Feedforward Control 369
13.7 Practical Frequency Domain Noise Measurements 370
13.7.1 Preamplification . 370
13.7.2 Spectrum Estimation 372
13.7.3 Direct Measurement of Position Noise 373
13.7.4 Measurement of the External Disturbance . 375
13.8 Experimental Demonstration . 375
13.9 Time-Domain Noise Measurements . 379
13.9.1 Total Integrated Noise . 379
13.9.2 Estimating the Position Noise 381
13.9.3 Practical Considerations 383
13.9.4 Experimental Demonstration . 384
13.10 A Simple Method for Measuring the Resolution
of Nanopositioning Systems 386
13.11 Techniques for Improving Resolution . 388
13.12 Chapter Summary . 390
References . 391
14 Electrical Considerations 395
14.1 Introduction . 395
14.2 Bandwidth Limitations . 396
14.2.1 Passive Bandwidth Limitations . 396
14.2.2 Amplifier Bandwidth 398
14.2.3 Current and Power Limitations . 398
Contents xv14.3 Dual-Amplifier . 399
14.3.1 Circuit Operation 399
14.3.2 Range Considerations . 401
14.4 Electrical Design . 402
14.4.1 High-Voltage Stage . 402
14.4.2 Low-Voltage Stage . 404
14.4.3 Cabling and Interconnects 405
14.5 Chapter Summary . 407
References . 407
Index 40
Index
A
Acceleration, 285, 288
Actuation, 61
Actuator dynamics, 223
AFM imaging, 3, 195, 256, 261, 268, 308
Amplifier bandwidth, 398
Amplifier noise, 354
Analog implementation, 193
Atomic force microscope (AFM), 3
B
Bandwidth, 109, 396
C
Cables, 405
Calibration and nonlinearity, 105
Capacitive sensor, 127, 133
Charge drives, 317
Charge versus voltage, 332
Classical Prandlt-Ishlinksii model, 306
Closed-loop noise, 359
Closed-loop noise spectrum, 360
Command shaping, 275
Compliance, 65
Connectors, 405
Continuous random processes, 343
Correlation functions, 344
Creep, 7, 32, 35
Current, 398
D
Damping control, 230
Drift, 107
Dual-amplifier, 399
Dual-stage repetitive control, 201
Duhem model, 301
Dynamics inversion, 253
E
Eddy-current sensor, 134
Electrical considerations, 395
Electrothermal sensor, 133
Environment, 58
Expected value, 339
External noise, 354
F
Failure considerations, 74
Feedback control, 10, 277, 292
Feedback versus feedforward control, 369
Feedforward and feedback control, 258
Feedforward control, 12, 240, 251, 292
Feedforward hysteresis compensation, 307
Filtered random processes, 347
Finite element analysis, 75
Flexure hinges, 62
Force feedback control, 221
Force sensor dynamics, 225
Force sensor noise, 226
Fourier series, 282
Frequency domain cost functions, 282
Frequency weighted objectives, 288
G
Gaussian random processes, 344
Gaussian random variables, 341
A. J. Fleming and K. K. Leang, Design, Modeling and Control 409
of Nanopositioning Systems, Advances in Industrial Control,
DOI: 10.1007/978-3-319-06617-2, © Springer International Publishing Switzerland 2014410 Index
H
Hysteresis, 7, 31, 205, 252
Hysteresis modeling and control, 299
I
Interferometer, 140
Inversion, 276
Iterative feedforward control, 261
J
Joint density functions, 343
L
Laser interferometer, 140
Linear encoder, 144
Linear variable displacement transformers
(LVDTs), 137
M
Manufacturing, 78
Materials, 75
Maxwell slip model, 300
Mechanical design, 57
Mechanical dynamics, 227
MEMs sensors, 133
Metrological traceability, 117
Minimizing signal power, 283
Minimizing velocity and acceleration, 285
Minimum acceleration, 288
Minimum velocity, 287
Model-based ILC, 265
Modeling, 223, 252
Modeling hysteresis, 300
Moments, 339
N
Nanometer position sensors, 118
Nanopositioner types, 43
Noise, 188, 337, 351
Noise measurement, 370, 373, 382, 386
Noise performance, 245
Noise sensitivity functions, 359
Nonlinear ILC, 267
O
Optimal inputs, 279
P
Parallel kinematic, 83
PI control, 180, 364
PI control with IRC damping, 183
PI control with notch filters, 181, 366
Piezoelectric actuator mounting, 27, 84
Piezoelectric compositions, 20
Piezoelectric manufacture, 22
Piezoelectric sensor, 123
Piezoelectric stack, 47, 322
Piezoelectric transducers, 17, 23
Piezoelectric tube, 43, 45, 166, 325
Piezoelectricity, 17
Piezoresistive sensors, 121
Polynomial model, 300
Position sensors, 103
Power, 398
Power spectral density, 345
Prandlt-Ishlinksii model, 309
Preamplification, 370
Preisach model, 302
Preload, 29, 85
Presiach model, 307
Probability distributions, 339
R
Random processes, 338
Repetitive control, 196
Resistive strain sensors, 118
Resolution, 113, 188, 351
Resonance, 9
Root-mean-square (RMS), 339
S
Scan generation, 288
Scanning probe microscope (SPM), 3
Self heating, 30
Sensor characteristics, 105
Sensor comparison, 147
Sensor noise, 110, 353
Serial kinematic, 79, 83
Shunt circuit implementation, 164
Shunt circuit modeling, 157
Shunt control, 155
Shunt damping, 159
Shunt design, 163
Signal optimization, 280
Spectral density, 349
Spectrum estimation, 372
Speed limitations, 81
Stability, 107Index 411
Stationarity, 343
Synthetic impedance, 164
T
Temperature dependence, 33
Thermal drift, 8
Thermal sensor, 133
Thermal stability, 77
Time domain cost function, 286
Time domain noise, 379
Total integrated noise, 379
Tracking control, 232
V
Variance, 339
Velocity, 285, 287
Vibration, 35
W
White noise, 348


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